3:17 you forgot dx!!!! xD

@Hauketal

6 жыл бұрын

Devansh Sehta Also a typo at 0:22 and one in the first description sentence.

@AhirZamanSairi

3 жыл бұрын

😂🤣

More wowed by this Kempner series than the ant... Never knew that.

@TippingPointMath

6 жыл бұрын

Kempner is pretty cool. See en.wikipedia.org/wiki/Kempner_series for the proof.

@blostrfig2690

3 жыл бұрын

@@TippingPointMath the summ of 1 on the gaps between all the perfecte numbers Is:1÷22+1÷461etc....=0,047722354....i wanted puplished but i don't have the account so now i puplished ere.

@blostrfig2690

3 жыл бұрын

Creditor Marco Ripà

Anyone else remember when Numberphile did the ant puzzle?

@tonydai782

6 жыл бұрын

me

@InterPixelYoutube

3 жыл бұрын

@@tonydai782 me

Ah, great video, looking forward to the next one

This really made me understand it better, thanks.

Okay how is this almost the exact same problem I thought of like 10 years ago and shared with barely anyone? Nice video

This was pretty fun! Welsh labs is doing a similar series, too.

Great video, as always! You always offer a unique perspective of these concepts: even if I'm familiar already with the concept itself, I find myself always learning something new! For instance, the Kempner (correct spelling?) series is new to me. But what is strange is that the removal of all reciprocals of multiples of 9 from the Harmonic Series causes convergence, whereas removal of reciprocals of primes from the series does not cause convergence. Does this mean that the number of total primes is less than 1/9th of all natural numbers?

@nayutaito9421

6 жыл бұрын

Prime numbers get rarer and rarer as the number increases. In this sense, for any natural number n, you can say the number of total primes is less than 1/n of all natural numbers.

@mail2hubertco

5 жыл бұрын

The video actually talks about the removal of all composite reciprocals (leaving only prime reciprocals). But, the sum of all composite reciprocals is also divergent. The result of the sum of all prime reciprocals is more interesting because prime numbers have a natural density of 0 (i.e. they become increasingly scarce by the PNT). It can easily be shown that the sum of the reciprocals of all composite numbers diverges by comparing it to half the harmonic series. math.stackexchange.com/questions/1733531/does-sum-of-the-reciprocals-of-all-the-composite-numbers-converge en.wikipedia.org/wiki/Natural_density

Miss ya

Great vid sir

Does this violin F design have mathematical properties to affect the harmonjcs/ sound of the violin? Great video. I do get lost with Algehra, though.

While you’re here fighting a headache while trying to wrap your brain around infinite series, remember that it may take you a while, but like the ant, you’ll get to the end eventually. Just have to remember to keep making that progress.

Thank you for more math videos.

Could you have any material that will give me information on this

interesting

Great video! Also, is 0:21 supposed to say "realtive"?

Kepner series is interesting

Lol Ants don't live that long. But I like it.

why the uploads have stopped?

Did you just solve the existential question of why we are alive and why we eventually die and what take us so long or quick to die!?!?!?!?

why hiatus

At the end you seem to go from expalining the harmonic series being divergent to the ant refach the end, but that would be convergent?

@bluecat16475

6 жыл бұрын

Daniel Sowsbery distance the ant has traveled at the end of any day n is Hn, the nth harmonic number. Since the harmonic series is divergent, the sum will eventually add up to infinity. Then trivially since it must add to infinity, it must add to 10m too. For any distance X there exists a day n such that Hn (the nth harmonic number) equal X.

2:58 does that mean that the first term is 0? Cause 1(1/1-1)= 1 (1/0)...so the 1st term doesn’t exist??

Did you just pronounce "phi" as "fee", but not "pi" as "pee", in the same sentence?

@TippingPointMath

6 жыл бұрын

Correct. In Greek, both are pronounced ending with "ee", but since the mathematical constant pi is very well-known as "pie", I think we're stuck with that pronunciation. I don't feel so constrained with phi.

@juggernaut93

6 жыл бұрын

3blue1brown just did the same in another video and there are similar comments there ahahah

@trejkaz

6 жыл бұрын

We all know you're only avoiding it because schoolkids would laugh. XD

@lizzybach4254

Жыл бұрын

I actually pronounce it as Phi as fee.

@trejkaz

Жыл бұрын

@@lizzybach4254 And pi?

im in pre-algebra. I give up trying to understand this

@ashleighholmes8422

6 жыл бұрын

dannyboy 1004 friend I’m in calculus and I didn’t know What was going on

Finally a video that my calculator can enjoy watching

gamma is the average distance between 2 randomly chosen points on a square

No more uploads...

Why am I watching this like I understand Anything?

@thephilosopher7173

3 жыл бұрын

Tbh he's explaining this as if you already have a background in Math. I love the topics this channel tries to go into, but the explanations are beyond simple lol.

faith in the ant

Help, I can't get Excel to replicate this. I agree for Ln(n)=10 that n=22026 (which gives the 60.3 years). However, when I try summing 1/1+1/2+1/3+1/4..... in Excel (which I can see is working to 15 significant digits), I end up with only n=12367 for the sum of 1/n=10. Also, Excel shows the sum of 1/n to n=22026 gives 10.577. What went wrong? edited to add simpler examples: 1/1+1/2+1/3+1/4+1/6+1/7+1/8+1/9+1/10=2.9290, but Ln(10)=2.3026, which is already less than 1/1+1/2+1/3+1/4+1/5+1/6 (=2.45) Also, e^3=20.09, but the sum of 1/n from n=1 to 11 = 3.02

@TippingPointMath

6 жыл бұрын

In your example only adding up to 1/10, ln(10) is too rough an approximation. For the long one, I suspect that 15 digits is not enough accuracy, all the round offs make a difference.

@smeggyhead1

6 жыл бұрын

Thanks for the reply. Rounding errors is what I initially thought, which is why I confirmed the precision that Excel works down to, which is 15 significant digits (for my version anyway, confirmed by setting the displayed number to 30 significant digits and seeing where the fractional recursions end). So that level of error, 22,000 times, should result with no error within 9 decimal places (likely a lot further out due to the round-ups and round-downs largely statistically cancelling). However, the apparent error totals to be in the first decimal place. So it doesn't make sense that Excel's 'rounding errors' is the answer. Does that make sense?

@supergreatsuper

5 жыл бұрын

@@smeggyhead1 The limit as n goes to infinity of H_n-ln(n) is a constant, usually denoted by the greek lowercase letter gamma, and is called Euler's constant. If you type in e^(10-gamma) into Google, the output is about 12366.9, which is much closer to your number. (You can visualize gamma as follows: at 2:47 in the video, the nth harmonic number is the area under the rectangles as x goes from 1 to n+1; ln(n) is the area under the curve as x goes from 1 to n. So H_n-ln(n) is the area in the rectangles that is not under the curve from 1 to n plus the area of the next rectangle, and gamma is the total area in the rectangles that are not under the curve. So when n is as large as 10,000, gamma is a very good approximation to H_n-ln(n).) Fun fact: It is still an open problem whether or not gamma is irrational.

The ant will get there in the end...

1 divided by infinity = 0.infinity

Rip channel

I am conuse about this.. I used asian flute as instrument how i acn relate it to math..

...What?

I see how this is amazing, but I will trust you to understand it. Thanks, regardless. It is as if you are speaking alien. There is something in my brain that is freaked out and paralyzed by math. Perhaps the math part is missing alltogether. After watching this twice, I have no clue why an ant would be walking on a stretching rubber band or what this has to do with harmonics or what one thing has to do with the other. I know it is terrible, but not worth learning math over. Everyone has an Achilles heel, and I would instead mine be math than have to learn math. As it relates to symbolic logic, maybe I will make an exception. "Let x equal x" is a maxim that has served me well. Thank you universe for creating engineers and mathematicians to do this thinking for the rest of us.

@aspiringcloudexpert5127

5 жыл бұрын

You shouldn't give up on math - there is an incredible and beautiful intuition, imagination and truth to math that really is worth the mental effort. If you are struggling with math, I would suggest you take some basic math courses on the Khan Academy website. Sal Khan (the creator of Khan Academy) explains math in a really simple and intuitive way. Also, it's all free. Side note: you might have Dyscalculia in which case please disregard all of the above. In any case, I wish you the best of luck. DFTBA!

@thephilosopher7173

3 жыл бұрын

Over the years I've realized its because of the way some ppl have tried to explain it, but also how I personally imagined it. Both cause you to lose it entirely. To better understand math you need to find videos that help you imagine what's being done, because all of math is just reasoning steming from: You have 1 Apple and theres another Apple. How many Apples are there? You can take this example and others and visualize math in a totally new (yet old) way.

When you sum all the non negative components of the Harmonic series, they converge to 0. This is a contradiction. A sum of non negative numbers can not sum to 0. The Harmonic series must diverge

man

ded